Question: Simplify the following expression: $ q = \dfrac{-a}{a - 7} - \dfrac{5}{7} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-a}{a - 7} \times \dfrac{7}{7} = \dfrac{-7a}{7a - 49} $ Multiply the second expression by $\dfrac{a - 7}{a - 7}$ $ \dfrac{5}{7} \times \dfrac{a - 7}{a - 7} = \dfrac{5a - 35}{7a - 49} $ Therefore $ q = \dfrac{-7a}{7a - 49} - \dfrac{5a - 35}{7a - 49} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-7a - (5a - 35) }{7a - 49} $ Distribute the negative sign: $q = \dfrac{-7a - 5a + 35}{7a - 49}$ $q = \dfrac{-12a + 35}{7a - 49}$